Heterogeneous multiscale methods for rough-wall laminar viscous flow

TL;DR

This paper introduces multiscale numerical methods to derive effective boundary conditions for laminar viscous flow over rough walls, combining high-resolution boundary simulations with coarser interior models, validated through analysis and experiments.

Contribution

The paper presents a novel multiscale approach that accurately computes wall laws for rough-wall laminar flow, integrating asymptotic analysis with numerical simulations.

Findings

Method recovers slip constant consistent with homogenization theory

Numerical experiments demonstrate applicability to various roughness patterns

Framework effectively couples boundary and interior flow simulations

Abstract

We develop numerical multiscale methods for viscous boundary layer flow. The goal is to derive effective boundary conditions, or wall laws, through high resolution simulations localized to the boundary coupled to a coarser simulation in the domain interior. The multiscale framework is analyzed in the context of laminar flow over a rough boundary. Asymptotic analysis shows that, up to a small perturbation, the method recovers the slip constant in the wall law derived from periodic homogenization theory. Numerical experiments illustrate the utility of the method for more general roughness patterns and fair field flow conditions.